Post on 12-Jan-2016
description
transcript
-Ray Emission ProbabilitiesEdgardo Browne
Decay Data Evaluation Project Workshop
May 12 – 14, 2008Bucharest, Romania
• Photon energy and intensity• Transition energy and intensity• Relative and absolute intensities
• Photon energy and intensity
Guidelines
• When possible use evaluated values:
Recommended standards for -ray energy calibration
(1999), R.G. Helmer, C. van der Leun, Nucl. Instrum. and
Methods in Phys. Res. A450, 35 (2000)
Update of X-ray and gamma-ray decay data standards for
detector calibration and other applications. IAEA - Report,
Vienna 2007.
Guidelines
• Weighted averages of values from the same type of
measurements (e.g. with Ge detectors).
• The uncertainty on the average (recommended)
value should not be smaller than the smallest input
uncertainty.
• For discrepant data use the “Limitation of Relative
Statistical Weight” method (Program LWEIGHT).
• Transition Energy
ET = E + ER,
where
ER = E2/2 MRc2 is the nuclear recoil energy
Eis the photon energy (in MeV)
MR ~ A is the mass of the daughter nucleus
MR c2 ~ 931.5 x A
• Transition Intensity
IT = I (1 + ),
where
Iis the photon intensity,
is the total conversion coefficient (theoretical interpolated value)
• Relative and Absolute Intensities
• Relative intensities (relative to the intensity of the strongest ray, usually taken as 100). Also called relative emission probabilities.
• Absolute intensities (per 100 disintegrations of the emitting radionuclide, usually given in %). Also called absolute emission probabilities, usually given “per decay.”)
1993Al15, 1994En02 2000He14 FittedE(keV) E(keV) E(keV)Unevaluated Evaluated 2173.334 (18) 2173.319 (15)
2173.319 (15)
2189.631 (9) 2189.616 (6) 2189.616 (6)2213.19 (11) 2213.181 (9) 2213.181 (9)2265.86 (24) 2265.84 (24)2292.188 (13)
2292.171 (13)
2341.691 (11) 2341.673 (11)
2393.153 (10) 2393.129 (7) 2393.129 (7)2422.544 (9) 2422.525 (7) 2422.525 (7)2433.826 (18)
2433.807 (18)
2467.99 (7) 2467.97 (7)2492.44 (3) 2492.42 (3)2537.11 (5) 2537.09 (5)2588.573 (13)
2588.553 (13)
2631.46 (9) 2631.44 (9)2698.94 (5) 2698.92 (5)2713.75 (5) 2713.73 (5)2751.852 (6) 2751.835 (5) 2751.835 (5)2780.12 (18) 2780.095 (16)
2780.095 (16)
2785.7 (3) 2785.7 (3)2802.8 (5) 2802.8 (5)2843.153 (16)
2843.130 (16)
66Ga -ray energies
Combining evaluated and unevaluated energies
66Ga Relative -Ray Intensities
Absolute -Ray Emission Probabilities
Ice(1039)/I+(gs) = 2.08 (10)x10-4 (experimental, 1960Sc06)
I+(gs)/Ii+ = 0.8697 (experimental, 1960Sc06)
Ice(1039,E2)/I(1039) = 2.69 (8)x10-4 (Theory, 1978Ro22)
Therefore
I(1039)/ Ii+ = 2.08 (10)x10-4 x 0.8697/ 2.69 (8)x10-4 =0.67(4)
Also Ii+/ Ii = 1.265 (from decay scheme and theoretical Ii+/Ii).
Since Ii+ + Ii = 100%, then Ii+ = 55.8 (24)%, and
I(1039) = 0.67 (4) x 55.8 (24) = 37 (3)%
233Pa - decay
I(312) = 38.6 (5) % (experimental value, Gehrke et al.)
I(+ce) (gs) = 102 (2) %
- 5-12%
What went wrong?
E(keV) T(exp.) T(theo. M1)
300 0.83 (2) 1.04
312 0.79 (2) 0.96
340 0.61 (2) 0.75
Answer: Nuclear penetration effects
Using X rays to normalize a decay scheme
231U -ray spectrum
I(25)=100 (6)
I(84)=50 (3)
IKX=390 (14) EC(K)/EC(Total) = 0.59
K = 0.972
BK=115.6 keV, thus most K-x rays originate from vacancies producedby the electron-capture process.
Total vacancies = IKX EC(Total) / K EC(K) = 680 (33)
Normalization factor N = 100 / 680 (33) = 0.147 (7)
I(25)=100 (6) x 0.147 (7) = 15 (1)%
I(84)=50 (3) x 0.147 (7) = 7.5 (6)%
192Ir and electron capture decay
E(keV) I I206 4.01 (6) 0.305 (9) 5.23 (8)489 0.527 (9)0.0242 (7) 0.540 (9) = 5.77 (8)316 100.0 (5)0.085 (3) 108.5 (6)468 57.76 (20) 0.0294 (9) 58.43 (20)612 6.365 (25) 0.0155 (5) 6.464 (25) = 114.9 (6)
The normalization factor is:
N = 100 / [I(489) (1+489) + I(206) (1+206) + I(316) (1+316) + I(612) (1+612)]
= 100 / 120.7 (7) = 0.828 (5)
N = 0.828 (5)
The electron capture and decay branchings are:
= 100 [I(489) (1+489) + I(206) (1+206)] /120.7 (7) =
100 / [1 + (I(316) (1+316) + I(612) (1+612)/(I(489) (1+489) + I(206) (1+206)) =
100 / [1 + 114.9 (6)/5.77 (8)] = 100 / 20.9 (3) = 4.78 (7)%
= 100 – EC = 100 – 4.78 (7) = 95.22 (7)%
= 95.22 (7)%
= 4.78 (7)%
125Sb Decay Scheme
It takes about a year for the intensity of the 109-keV ray to be in equilibrium (within 1%) with the other rays. The intensityof the 35-keV ray is also affected by the 58-year half-life ofthe 144-keV 125mTc isomer.
Decay Scheme Normalization
• [ I (1 + i) (gs and 144-keV level)] N =100%
• N = 0.2955 (24)
• The equilibrium correction for I(109) is
[T1/2(125Sb) – T1/2(125mTe)/ T1/2(125Sb) ]= 0.943.
- feeding to the 144-keV 125mTe isomer
• I-=[I(109)(1+109) x 0.943 – I(176) (1+176) –
I(380)(1+380) – I(497)(1+497)] N
• I-= 13.4%
Absolute -Ray Intensities Deduced from Decay Scheme
Decay Branching Ratios
Assuming EC(gs) = -(gs) = 0%
-ray transition intensity balance
The corresponding normalization factor is
N = 100 / [ Ii(out) + Ii(gs) – Ii(in)] =
100 / [ Ii(out) – Ii(in)] + Ii(gs), but
[ Ii(out) – Ii(in)] = 0, therefore
N = 100 / Ii(gs)
Ii(out)
Ii(in)
Ii(gs) 0
Ii
Uncertainties of Absolute -Ray Emission Probabilities Deduced from Decay Scheme
I1 + dI1 I2 + dI2
(I1 + I2) N = 100%
N = 100 / (I1 + I2)
The absolute emission probabilities are
I1(%) = 100 x I1/(I1 + I2)
I2(%) = 100 x I2/(I1 + I2),
Their uncertainties have the same value, irrespective of their values in the relative
emission probabilities!!
dI1(%)2=dI2(%)2= 104 x (I12 dI2
2+I1dI22)/(I1+I2)2
If I1 = I2 = I, and dI1 = dI2 = dI,
then
dI1(%)/I1(%) = dI2(%)/I2(%) = [(2)1/2/2] dI/I
The fractional uncertainties are smaller than those in the corresponding relative spectral
emission probabilities!!
SeeNucl. Instr. and Meth. In Phys. Res. A249, 461 (1986)
for general mathematical formulae.
240Am EC Decay to 240Pu
E2 E2 (<1% M1)
988 889
99 – E2
43 – E20+
2+
4+
3+
0
142
43
1031
Pu240
240 Am
3- 50.8 h 0
6561 y
240Am Gamma Rays
1972Ah07 1971LeZO 1972PoZS Recommended ValuesE(keV) I(rel) E(keV) I(rel) keV) I(rel) E(keV) I(rel) I(abs)
42.9 (1) 0.09 (1) 42.87 (4)* 0.09 (1)^ 0.110 (3)
98.9 (1) 1.5 (2) 98.9 (1)# 1.5 (2)^ 1.49 (3)
152.4 (10) 0.012 (3) 152.4 (10)† 0.012 (3)‡ 0.012 (3)
249.7 (10) 0.020 (3) 249.7 (10)† 0.020 (3)‡ 0.020 (3)
251.8 (10) 0.005 (2) 251.8 (10)† 0.005 (2) 0.0049 (20)
303.7 (10) 0.009 (2) 305.3 (10) 0.073 304.5 (10)& 0.009 (2)‡ 0.009 (2)
343.7 (10) 0.049 (5) 343.7 (10) 0.095 343.7 (10)& 0.049 (5)‡ 0.048 (5)
382.1 (10) 0.053 (5) 382.3 (10) 0.051 382.2 (10)& 0.053 (5)‡ 0.052 (5)
447.8 (10) 0.013 (4) 447.8 (10)† 0.013 (4)‡ 0.013 (4)
507.9 (10) 0.072 (6) 508.2 (10) 0.073 508.0 (10)& 0.072 (6)‡ 0.071 (6)
555.4 (10) 0.010 (5) 555.4 (10)† 0.010 (5)‡ 0.010 (5)
600.7 (10) 0.014 (6) 600.7 (10)† 0.014 (6)‡ 0.014 (6)
606.7 (10) 0.070 (8) 606.9 (10) 0.055 606.8 (10)& 0.070 (8)‡ 0.069 (8)
697.8 0.035 (8) 697.8† 0.035 (8)‡ 0.035 (8)888.7 (1) 25.1 (9) 888.83 (5) 25.1 (4) 888.91 (5) 25 888.85 (5)@ 25.1 (4)• 24.7 (5)916.2 (3) 0.10 (1) 916.1 (2) 0.087 (6) 917.1 (2) 0.07 916.5 (3@) 0.090 (6)• 0.089 (6)
934.6 (5) 0.025 (3) 935.7 (5) 0.032 935.2 (6)& 0.025 (3)‡ 0.025 (3)
938.0 (6) 0.007 (3) 938.2 (10) 0.0054 938.0 (5)& 0.007 (3)‡ 0.007 (3)959.4 (3) 0.005 (1) 959.1 (5) 0.037 (4) 960.2 (2) 0.022 959.9 (3)@ 0.039 (4)• 0.038 (5)987.7 (1) 73.3 (25) 987.79 (6) 73.2 (10) 987.84 (6) 73.2 987.80 (4)@ 73.2 (10)• 72.2 (6)1033.4 (5) 0.011 (2) 1033.5 (3) 0.010 (1) 1034 (1) 0.0095 1033.5 (2)@ 0.010 (1)• 0.0099 (10)1036.3 (4) 0.017 (3) 1036.0 (3) 0.015 (2) 1037 (1) 0.015 1036.2 (2)@ 0.016 (2)• 0.0157 (20)
1089.8 (10) 0.0031 (6) 1091.5 (10) 0.0029 1090.7 (8)& 0.0031 (6)‡ 0.0031 (6)
Normalization Procedures
1. Assumes (43) < 1%, (142) < 1%, and T(GS, 43, 142) > 98% (= 99 + 1%)
I(988) = 72.4 + 0.9 %
2. Assumes just (43) < 1%, and T(GS, 43) > 99% (= 99.5 + 0.5%)
I(988) = 72.0 + 0.6 % Recommended value I(988) = 72.2 + 0.6 %
Program GABS
INPUT: ENSDF Data Set
OUTPUT: Absolute -Ray Intensities
REPORT FILE Current date: 03/09/2008
240AM EC DECAY NR= 0.984 13 BR= 1.00 FOR INTENSITY UNCERTAINTIES OF GAMMA RAYS NOT USED IN CALCULATING NR, COMBINE THE UNCERTAINTY IN THE RELATIVE INTENSITY IN QUADRATURE WITH THE UNCERTAINTY IN THE NORMALIZING FACTOR (NR x BR). FOR THE FOLLOWING GAMMA RAYS: E= 42.87 4 %IG=0.1092 24 PER 100 DECAYS. E= 98.9 1 %IG=1.486 23 PER 100 DECAYS.(Compare with 1.49 3) E= 152.4 10 %IG=0.012 3 PER 100 DECAYS. E= 555.4 10 %IG=0.010 5 PER 100 DECAYS.(Compare with 0.010 5) E= 597.40 7 %IG=0.006 3 PER 100 DECAYS. E= 507.9 10 %IG=0.071 6 PER 100 DECAYS. E= 606.7 10 %IG=0.069 8 PER 100 DECAYS.(Compare with 0.069 8) E= 447.8 10 %IG=0.013 4 PER 100 DECAYS. E= 600.7 10 %IG=0.014 6 PER 100 DECAYS. E= 251.8 10 %IG=0.0049 20 PER 100 DECAYS. E= 303.7 10 %IG=0.0089 20 PER 100 DECAYS. E= 758.61 8 %IG=0.01033 13 PER 100 DECAYS. E= 857.48 10 %IG=0.00394 5 PER 100 DECAYS. E= 900.37 10 %IG=0.001476 19 PER 100 DECAYS. E= 916.1 2 %IG=0.089 6 PER 100 DECAYS.(Compare with 0.089 6) E= 249.7 10 %IG=0.020 3 PER 100 DECAYS. E= 343.7 10 %IG=0.048 5 PER 100 DECAYS. E= 697.8 %IG=0.034 8 PER 100 DECAYS. E= 959.3 3 %IG=0.038 5 PER 100 DECAYS.(Compare with 0.038 5) E= 382.1 10 %IG=0.052 5 PER 100 DECAYS. E= 888.85 5 %IG=24.7 5 PER 100 DECAYS. E= 987.79 6 %IG=72.0 6 PER 100 DECAYS.(Compare with 72.0 14) E= 934.6 5 %IG=0.025 3 PER 100 DECAYS.